Question

If $A=\left[\begin{array}{ccc}0& x& 16\\ x& 5& 7\\ 0& 9& x\end{array}\right]$ is singular, then the possible values of $x$ are

• A. $0,\pm 12$
• B. $0,\pm 1$
• C. $0,\pm 4$
• D. $0,\pm 5$

Answer 1

Answer: (A)

$\left[\begin{array}{ccc}0& x& 16\\ x& 5& 7\\ 0& 9& x\end{array}\right]=0$
$\Rightarrow -x\left(x^2-144\right)=0$
$\Rightarrow x\left(x^2-144\right)=0$
$\Rightarrow x=0,x=\pm 12$